United won three and lost one in November, securing victories at home over Queen of the South and Alloa Athletic, as well as a 1-0 win over Ross County in Dingwall.
Neilson had enjoyed an unbeaten start to his tenure as United boss until last Friday’s 5-0 defeat at home to Ayr United.
Summer signing Aird, 23, has scored three goals and added 13 assists, and is the first Tannadice player to win the award since Scott Fraser in November last year.
The last United manager to be awarded the monthly prize was Ray McKinnon in November 2016.
The Terrors currently lie third in the Scottish second tier; six points off leaders Ayr and five points ahead of fourth-placed Inverness.